a copper wire of diameter 6mm is evenly wrapped on a cylinder of length 15cm and diameter 49cm to cover its whole surface . find the length and volume of the wire. if the specific gravity of copper be 9kg per cu cm , find the weight of the wire.

Length of cylinder = 15 cm = 150 mm

Diameter of cylinder = 49 cm = 490 mm

Number of turns of copper wire = $\frac{150}{6}=25$

Length of one turn = $2\mathrm{\pi}\left(\frac{490}{2}\right)=490\times \frac{22}{7}=1540\mathrm{mm}$

So total length of copper wire = $25\times 1540mm=38500mm$

Therefore volume of copper wire = $\mathrm{\pi}\times {\left(3\right)}^{2}\times 38500{\mathrm{mm}}^{3}=1089000{\mathrm{mm}}^{3}$

Volume ( in cubic centimetres ) = 1089 $c{m}^{3}$

Specific gravity of wire = $9kg/c{m}^{3}$

So weight of wire = $\left(1089\times 9\right)kg=9801kg$

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